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    "### 3.1 Matrices and vectors\n",
    "\n",
    "* matrices:$m\\times n,eg:A,B,C...$\n",
    "\n",
    "* vectors $n\\times 1,eg:a,b,c...$\n",
    "\n",
    "* 默认下标使用1开始\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Addition and scalar multiplication\n",
    "\n",
    "* addition\n",
    "\n",
    "![](../pic/QQ截图20201021143444.png)\n",
    "\n",
    "* scalar multiplication\n",
    "\n",
    "$$\n",
    "3 \\times\\left[ \\begin{matrix} 1 & 2 & 3 \\\\ 4 & 5 & 6 \\\\ 7 & 8 & 9 \\end{matrix} \\right] \\tag{3}\\\\\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 multiplication\n",
    "\n",
    "* Matrices-vectors\n",
    "\n",
    "![](../pic/QQ截图20201021143754.png)\n",
    "\n",
    "* Matrices-Matrices\n",
    "\n",
    "![](../pic/QQ截图20201021144230.png)\n",
    "\n",
    "* additional\n",
    "\n",
    "$A\\times B \\neq B\\times A$\n",
    "\n",
    "$A\\times (B \\times C) = (A\\times B) \\times C$\n",
    "\n",
    "$A\\cdot I = I\\cdot A = A$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 Inverse and transpose\n",
    "\n",
    "* Inverse\n",
    "\n",
    "* transpose"
   ]
  },
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